California    Academy    of    Soieaoea 
Carl  Ewald  Gruneky  Bequest 
August  I,  1034 


i 


The  Venturi  Meter 


BUILDERS    IRON    FOUNDRY 
PROVIDENCE,  R.  I.,  U.  S.  A. 


o  en 

^ 


THE   VENTURI    METER 


PATENTED    BY 
& 

CLEMENS    HERSCHEL 

HYDRAULIC  ENGINEER 

AND 
BUILDERS    IRON    FOUNDRY 


MADE    BY 


BUILDERS   IRON   FOUNDRY 

FOUNDERS     AND     MACHINISTS 


PROVIDENCE,  R.  I.,  u.  s.  A. 
1898. 


COPYRIGHTED,    1898,    BY    BUILDERS  IRON    FOUNDRY,     PROVIDENCE,    R. 
PRESS    OF    LIVERMORE    &    KNIGHT    CO.,    PROVIDENCE,    R.    !. 


PREFACE 


In  the  papers  that  have  hitherto  been  published 
by  us  concerning  the  Venturi  Meter,  (copies  of 
which  will  be  furnished  upon  application),  we  have 
given  a  more  or  less  technical  explanation  of  the 
physical  laws  governing  the  action  of  the  meter, 
and  called  attention  to  the  uses  to  which  it  could 
be  applied.  The  object  of  this  pamphlet  is  to 
again  state  the  facts  relating  to  the  operation  of 
the  meter,  as  briefly  as  possible,  and  to  show  by 
some  illustrations  how  it  has  been  applied  in  actual 
uses. 

BUILDERS  IRON  FOUNDRY. 


PROVIDENCE,  R.  I.,  January  i,  1898. 


THE  VENTURI   METER 


The  Meter  is  named  for  the   Italian  philosopher  ongin  of  name. 
Venturi,  who  first  called  attention,    in    1796,  to  the 
relation  between  the  velocities  and  pressures  of  fluids 
when     flowing    through     converging    and     diverging 
tubes. 

The    Meter    consists    of    two    parts — the    Tube,  Principal  parts 

.  .of  meter. 

through  which  the  water  flows,  and  the  Register,  which 
sums  up  and  indicates  on  a  dial  the  quantity  of  water 
that  has  passed  through  the  tube. 

The  Tube  is  formed  of  two  truncated  cones,  The  Tube,  its 
joined  at  their  smallest  diameters  by  a  short  throat 
piece.  At  the  upstream  end  and  at  the  throat  there 
are  encircling  pressure  chambers  that  are  connected 
with  the  interior  by  carefully  drilled  holes,  and  from 
which  pressure  pipes  lead  to  the  register.  See  Figure  i . 

The  operation  of  the  Venturi  Meter  is  due  to  the  operation  of  the 
fact  that  when  water  in   any   pipe   passes  from  a  state 
of  rest  to  movement,  or  from  one  velocity  of  flow  to  a 
greater  velocity,  a  certain  amount  of  pressure  against 
the  shell  of  the  pipe  disappears,  and  that  the  disap-  velocities. 
pearance    of  pressure,    or    loss    of  head,    is    entirely 
dependent  upon  the  velocities  of  flow  past  the  points 
in  the  pipe  at  which  pressure  is  taken. 

Therefore,  at  two  points  in  a  taper  pipe,  or  Venturi 
tube,  as  at   U-T,  Figure  i,  because  of  different  sec- 


VENTURI   METER 


FIGURE  i. 
SECTIONAL  VIEW  OF  VENTURI  METER  TUBE  AND  REGISTER. 


tional  area,  different  velocities  and  consequently  differ- 
ent pressures  must  exist  whenever  there  is  any  flow 
through  the  tube.  The  difference  in  pressure  at  the 
two  points  is  always  the  same  for  the  same  velocity 
of  flow,  whatever  the  total  or  hydraulic  pressure  may 
be;  and  by  exhaustive  experiment  has  been  shown  to 
be  nearly  equal  (in  feet  of  water)  to  1-64  the  square 
of  the  velocity  of  flow  (in  feet  per  second)  through 
throat  of  meter  tube;  or,  in  other  words,  to  coincide 
closely  with  the  fundamental  hydraulic  formula  for 
the  head  corresponding  to  any  velocity  of  discharge 
from  an  orifice, 


in  which  "h"  corresponds  to  the  difference  in  pressure 
at  U  and  T,  V  the  velocity  of  flow  through  throat, 
and  g  the  acceleration  of  gravity. 

For  demonstration  of  the  preceding  statements,  see  Herschel's 
Rowland  Prize  Paper,  Transactions  of  American  Society  of  Civil 
Engineers,  December,  1877.      Reprint  furnished  on  application. 
Merriman's  Hydraulics,  Article  71,  (Reprinted  herewith.) 
Illustrations    of    the    Theorem    of  Bernouilli  under  "  Hydro- 
mechanics," —  Qth   Edition  Encyclopaedia  Britannica,  or   reprint 
furnished  on  application,  and  almost  any  modern  text  book  on 
Hydraulics. 

The  different  pressures  existing  at  the  upstream  Register. 
end  and  throat  of  the  meter  tube  are  transmitted  by 
small  pipes  T—  U,  to  the  register  (Figure  i),  where 
they  oppose  one  another,  and  are  balanced  by  dis- 
placement of  level  of  two  columns  of  mercury  in 
cylindrical  tubes,  one  within  the  other.  The  inner 
mercury  column  carries  a  float,  J,  V,  the  position 
of  which  is  dependent  on,  and  as  previously  explained 
is  an  indication  of  the  velocity  of  water  flowing  through 


FIGURE  2.     REGISTER. 


the  tube.  The  position  assumed  by  an  idler  wheel  H 
carried  by  this  float,  relative  to  an  intermittently  re- 
volving integrating  drum  I,  determines  the  duration 
of  contact  of  gears  G  and  F  connecting  drum  and 
counter,  by  which  the  flow  for  successive  intervals  is 
registered. 

It  is  a  common  but  erroneous  impression  that  water  common  error 

n    •      •  i  i  •      '         •  i      •  '  j     regarding  loss  of 

flowing  through  a  contracting  pipe  brings  an  increased  head 
pressure  against  the  entire  converging  surface  which  it 
meets.  The  reverse  of  this  impression  is  true.  The 
pressure  of  water  flowing  through  the  Venturi  Tube 
decreases  from  the  inlet  to  the  throat,  and  increases  from 
the  throat  to  the  outlet.  The  difference  between  pres- 
sures at  inlet  and  outlet  ends  of  the  Tube  is  the  friction 
head  or  loss  of  head  caused  by  its  operation,  and  under 
ordinary  circumstances  is  inconsiderable.  The  amount 


/-       i    •         i  •  i  -11  r  '         *        inconsiderable. 

of  this  loss  in  tubes  with  throat  area  1-9  of  main  is 
stated  in  the  accompanying  tables  and  shown  by  dia- 
gram, Figure  10.  By  adaptation  of  the  tube  to  re- 
quirements, the  loss  of  head  may  be  limited  to  any 
desired  amount. 

There  is  no  limit  to  the  size   of  the  meter   tubes,  Advantage  of 
nor  the  quantity  of  water  that  may  be  measured.     The  ™l™~™ 
largest  that  has  yet  been  made  is  9  feet  diameter,  with 
maximum  capacity  at  the  rate  of  more  than  200,000,000 
gallons  in  24  hours. 

Usually  the  meter  tubes,  for  sizes  under  60  inches 
diameter,  are  made  of  cast  iron,  with  bronze-lined  throat 
pieces,  but  for  special  service  may  be  made  of  wooden 
staves,  sheet  steel,  cement-concrete,  brick  or  other 
material,  with  suitable  metal  parts  for  throat  and  up- 
steam  pressure  chambers. 

The  tube  is  usually  laid  as  a  part  of  the  pipe  line  Meter  not 
and  is    not  injuriously  affected  by  water  hammer  or 


stances  in  the 


FIGURE  3. 
BACK  OF  REGISTER. 


the  most  violent  fluctuations  of  velocity  or  pressure, 
and  requires  no  more  care  than  the  pipe  line  itself. 
The  meter  cannot  be  disarranged  by  fish,  gravel  or  other 
substances  carried  through  the  pipe  line  by  the  water. 

The  meter  may  be  said  to  have  created  a  field  of  General u 

J  ness. 

usefulness  for  water  meters  which  did  not  previously 
exist.  It  accomplishes  with  little  difficulty  what  otherwise 
is  done  only  laboriously  or  approximately  and  clumsily. 

In  water  works,  this  meter  enables  a  record  to  be  Special ad 
kept    of   the    total    quantity   consumed,   also,   of  the 
quantities  consumed  by  large  users,  such   as  adjacent 
towns  and  cities,  the  several  districts   of  one  and  the 
same  city,  railroads,  factories  and  the  like.    See  Fig.  11. 

As  it  cannot  be  disarranged  by  substances  in  the  Fire  service. 
water,    it    is    especially    desirable,  when   the    water    it 
measures  is  liable  to  be  used  for  fire  service. 

It  can  be  used  as  a  "  waste-water  meter,"  keeping  a 
record  of  the  quantity  passing  the  meter  at  any  time. 
Its  use  in  the  detection  of  wastes  and  leaks,*  and  as  a 
measure  of  the  slip  of  pumps/)*  and  the  action  of  filter 
plants,  makes  it  very  valuable  to  all  works  for  a  pub- 
lic supply  of  water. 

A  similar  line  of  service  can  be  done  by  this  meter  special  adva 

i  c  f         i    •     i  tages  forsew 

in   the  case  or  sewerage  systems,  many  or  which,  as  agesystem. 
now  built,  are  constructed  and  operated  for  the  joint 
benefit  of  several  towns  and  cities,  with  the  cost  of 
operation  divided  pro  rata  between  them,  according  to 
the  quantity  of  sewage  contributed. 

For  irrigation  works  this  meter  can  accomplish  what  special  adva 
has  hitherto  been  desired  but  has  not  been  practicable,  [^work^ 
It  enables   water   for  irrigation   purposes   to    be    sold 
strictly  by  measure,  and  with  practically  no  constraint 
as  to  the  time  when  it  may  be  drawn. 

*See  Report  of  1896-97,  Water  Commissioners,  Clinton,  Mass. 
fSee  Report  of  Bureau  of  Water,  City  of  Philadelphia,  1896. 


I  I 


Special     advan- 
tages for  mills 
and  factories. 


In  the  case  of  water  powers,  this  meter  is  valuable 
in  determining  the  quantity  of  water  drawn  by  tenants 
of  water-rights  for  power,  or  for  wash  water  and  other 
purposes  other  than  power. 

It  offers  to  mills  and  factories  a  means  of  checking 
charges  for  power,  or  for  ascertaining  the  amount  of 
power  used.J  Figure  5.  It  can  be  submerged  in  a 
flume  or  penstock,  and  enables  large  bodies  of  water 
to  be  measured  regularly  and  accurately. 


4-lNCH  VENTURI  TUBE,  SPIGOT  ENDS. 


MEMORANDA 


Column  of  water  i  foot  high 
Column  of  water  i  foot  high 
cury  0.883  ms-  n^gh>  at  62°  F. 
Gallon 


Cubic  foot  of  water 
Cubic  foot  of  water 
Flow  at  rate  of  i  cubic  ft.  per 
646,000  gallons. 

2g  -  64.33 


=  0.433  lt>s-  at  62°  F. 
=  Column    of    Mer- 


231  cubic  ins. 
0.1337  cubic  foot. 
8.335lbs.at62°F. 
3.786  litres. 
7.480  gallons. 
62.355  lbs.at62°F. 
second  for  24  hours 


2      »       8.02 


JSee  Engineering  News,  Vol.  XXXVIII,  No.  2,  July 
Pioneer  Electric  Power  Co.,  at  Ogden,  Utah." 


1897.     "  The  Plant  of  the 


12 


FIGURE  5. 

ONE  OF  Two  54-INCH  VENTURI  METERS. 

POWER  STATION  PIONEER  ELECTRIC  POWER  Co. 

OGDEN,  UTAH. 


FIGURE  6. 
16-lNCH  VENTURI  METER  TUBE. 


FIGURE  7. 
20-lNCH  VENTURI  METER  TUBE. 


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TABLE  SHOWING  QUANTITY  OF  WATER  PASSING  THROUGH 
VENTURI  METER  TUBES  OF  DIFFERENT  SIZES 
(THROAT  AREA  1-9  OF  MAIN),  WITH  CORRESPOND- 
ING VELOCITY  OF  FLOW  IN  THROAT,  "  HEAD  ON 

VENTURI,"  AND  "  FRICTION  HEAD."* 


"  HEAD  ON  VENTURI "  is  the  difference  of  pressure, 
in  feet  of  water,  at  throat  and  up-stream  end  of  tube. 

"  FRICTION  HEAD  "  is  the  difference  of  pressure,  in  feet 
of  water,  at  up-stream  and  down-stream  ends  of  tube,  or 
the  LOSS  OF  HEAD  due  to  introduction  of  meter  tube. 


Vel.  through 
throat  in  ft. 
per  second 

Quantity  in  Cubic  Feet  per  Second. 

Head 
on 
Venturi, 
in  feet. 

Friction 
Head 
in  feet, 
approxi- 
mate. 

lo-inch 
Meter. 

12-inch 
Meter. 

i5-inch 
Meter. 

i6-inch 
Meter. 

i8-inch 
Meter. 

2O-inch 
Meter. 

2-5 

.152 

.218 

•340 

•389 

.490 

.608 

.097 

•015 

3- 

.182 

.261 

.408 

.466 

.589 

.728 

.14 

.02 

3-5 

.212 

•305 

•477 

•543 

.687 

.848 

.19 

.025 

4- 

.242 

.348 

•545 

.619 

.784 

.968 

•25 

•03 

5- 

•303 

.436 

.681 

•778 

.981 

1.  212 

•39 

•05 

6. 

•364 

.523 

.818 

•932 

.179 

1.456 

.56 

.07 

7- 

.424 

.6lO 

•954 

.086 

•374 

1.696 

.76 

.10 

8. 

.485 

.697 

.090 

•238 

-570 

1.940 

1.  00 

•13 

9- 

•545 

.785 

.227 

.398 

.767 

2.180 

1.20 

•17 

10. 

.606 

.872 

.362 

.556 

-963 

2.424 

1.50 

.22 

12. 

.727 

.047 

.636 

.864 

2-357 

2.908 

2.26 

.32 

14- 

.850 

.224 

.908 

2.172  1  2.748 

3.400 

3.10 

.42 

16. 

.970 

•396 

2.181 

2.476 

3-!4i 

3.880 

4-05 

•53 

18. 

.090 

•570 

2-454 

2.796 

3-534 

4.360 

5.16 

.67 

20. 

.212 

•745 

2.727 

3.II2 

3-927 

4.848 

6.40 

.82 

24. 

•450 

2.094 

3.272 

3.728 

4.712 

5.800 

9.21 

1.20 

28. 

.700 

2-443 

3-8i7 

4-344 

5-497 

6.800 

12.73 

1.68 

32- 

.940 

2.792 

4-363 

4-952 

6.287 

7.760 

17.25 

2.IO 

36. 

2.180 

3-Hi 

4.908 

5-592 

7.062 

8.720 

21.75 

2.70 

38. 

2.300 

3-3*6 

5.181 

5-9I3 

7-455 

9.200 

24.50 

3.00 

*  To  meet  special  requirements  as  to  Capacity  or  Friction  Head,  Meter  Tubes  are  made 
with  throats  of  any  area  less  than  one-fourth  the  area  of  main  pipe. 


TABLE  SHOWING  QUANTITY  OF  WATER  PASSING  THROUGH 
VENTURI  METER  TUBES  OF  DIFFERENT  SIZES 
(THROAT  AREA  1-9  OF  MAIN),  WITH  CORRESPOND- 
ING VELOCITY  OF  FLOW  IN  THROAT,  "  HEAD  ON 

VENTURI,"  AND  "  FRICTION  HEAD."* 


"  HEAD  ON  VENTURI"  is  the  difference  of  pressure, 
in  feet  of  water,  at  throat  and  up-stream  end  of  tube. 

"  FRICTION  HEAD"  is  the  difference  of  pressure,  in  feet 
of  water,  at  up-stream  and  down-stream  ends  of  tube,  or 
the  LOSS  OF  HEAD  due  to  introduction  of  meter  tube. 


Vel.   thro' 
throat 
in  feet 
per  sec. 

Quantity  in  Cubic  Feet  per  second. 

Head 

on 
Venturi, 
in  feet. 

Friction 
Head 
in  feet, 
approx- 
imate. 

2i-inch 
Meter. 

24-inch 
Meter. 

27-inch 
Meter. 

30-inch 
Meter. 

36-inch 
Meter. 

42-inch 
Meter. 

2.5 

.668 

.872 

I.IO4 

I-363 

1.963 

2.672 

•097 

.015 

3- 

.801 

1.046 

I-325 

1.636 

2-355 

3.207 

.14 

.02 

3-5 

•935 

1.  221 

I.546 

1.908 

2.748 

3-741 

.19 

-025 

4- 

1.069 

1.396 

1.767 

2.181 

3-I4I 

4.277 

.25 

•°3 

5- 

1.336 

1.744 

2.208 

2.727 

3-927 

5-345 

•39 

•°5 

6. 

1.603 

2.092 

2^650 

3-272 

4.712 

6.414 

•56 

.07 

7- 

1.871 

2-443 

3.092 

3.817 

5-497 

7.482 

•76 

.IO 

8. 

2.138 

2.792 

3-534 

4-363 

5-283 

8-552 

I.OO 

•13 

9- 

2.405 

3-I38 

3-976 

4.908 

7.068 

9.621 

i.  20 

•17 

10. 

2.672 

3.488 

4.417 

5-454 

7-854 

10.690 

1.50 

.22 

12. 

3.204 

4.188 

5-301 

6-545 

9-424 

12.828 

2.26 

•32 

14. 

3.740 

4.888 

6.184 

7-630 

10.995 

14.964 

3.10 

.42 

16. 

4.276 

5.585 

7.068 

8.727 

12.566 

17.104 

4-05 

•53 

18. 

4.812 

6.284 

7.952 

9.817 

H.I37 

19.242 

5.16 

-67 

20. 

5-345 

6.976 

8.835 

10.908 

15.708 

21.386 

6.40 

.82 

24. 

6.408 

8-377 

10.602 

13.090 

18.849 

25-656 

9.21 

1.20 

28. 

7.484 

9-773 

12.370 

15.271 

21.991 

29.932 

12.73 

1.68 

32. 

8.552 

1  1  .  1  70 

H.I37 

J7-453 

25-132 

34.208 

17.25 

2.10 

36. 

9.624 

12.566 

15.904 

19-635 

28.274 

38.484 

21-75 

2-70 

38. 

10-155 

13.264 

16.776 

20.725 

29.845 

40.622 

24.50 

3-oo 

*  To  meet  special  requirements  as  to  Capacity  or  Friction  Head,  Meter  Tubes  are  made 
with  throats  of  any  area  less  than  one-fourth  the  area  of  main  pipe. 


20 


TABLE  SHOWING  QUANTITY  OF  WATER  PASSING  THROUGH 
VENTURI    METER  TUBES   OF   DIFFERENT   SIZES 

(THROAT  AREA   1-9  OF  MAIN),  WITH  CORRESPOND- 
ING  VELOCITY   OF   FLOW    IN   THROAT,  "  HEAD  ON 

VENTURI,"  AND  "FRICTION  HEAD."* 


"  HEAD  ON  VENTURI  "  is  the  difference  of  pressure, 
in  feet  of  water,  at  throat  and  up-stream  end  of  tube. 

"  FRICTION  HEAD  "  is  the  difference  of  pressure,  in  feet 
of  water,  at  up-stream  and  down-stream  ends  of  tube,  or 
the  LOSS  OF  HEAD  due  to  introduction  of  meter  tube. 


Ill 

Quantity  in  Cubic  Feet  per  Second. 

Head 

on 

Friction 
Head 

•til 

48-inch 

54-inch 

6o-inch 

72-inch 

8o-inch 

Venturi, 
in  feet. 

in  feet, 
approxi- 

Meter. 

Meter. 

Meter. 

Meter. 

Meter. 

mate. 

2-5 

3-490 

4.417 

5-454 

7-854 

9.647 

.097 

.015 

3. 

4.188 

5-301 

6-545 

9-435 

11-577 

.14 

.02 

l.C 

4.886 

6.185 

7.640 

10.995 

I3-507 

.19 

•025 

J    -J 

4- 

5-585 

7.068 

8.728 

12.682 

I5-500 

•25 

•03 

5. 

6.981 

8.835 

10.906 

15.708 

19.295 

-39 

•05 

6. 

8-377 

IO.6O2 

13.090 

18.849 

23.154 

•56 

.07 

7. 

9.772 

12.370 

15.280 

21.990 

27.014 

-76 

.IO 

8. 

1  1  .  1  7O 

14.136 

I7-452 

23-364 

3I.OOO 

I.OO 

•13 

9- 

12.564 

15-903 

19-635 

25-305 

34-731 

i.  20 

•17 

10. 
12. 

13.962 
16.754 

17.670 
21.204 

21.816 
26.180 

31.416 
37.698 

38-390 
46.308 

1.50 
2.26 

.22 
•32 

14. 

19-554 

24.740 

30.560 

43.980 

54.028 

3.10 

.42 

16. 

18. 

20. 

22.340 
25.128 
27.924 

28.272 
31.806 
35-340 

34.904 
39.270 

50.728 
56.610 
62.832 

62.000 
69.462 
76.780 

4-05 

5.16 

6.40 

•53 
-67 
.82 

24. 
28. 

33-508 
39.088 

42.408 
49.480 

52.360 
61.120 

75-396 
87.960 

92.616 
108.046 

9.21 
12.73 

1.20 

1.68 

32- 
36. 

44.780 
50.256 

56-544 
63.612 

69.808 
78.549 

101.456 
II3-738 

124.000 
138.924 

17-25 

21-75 

2.IO 
2.70 

38- 

53-052 

67.146 

82.900 

119.442 

i47-!54 

24.50 

3.00 

*  To  meet  special  requirements  as  to  Capacity  or  Friction  Head,  Meter  Tubes  are  made 
fith  throats  of  any  area  less  than  one-fourth  the  area  of  main  pipe. 


21 


uosjwj  01  •     •- si/«y  wn  01 


ACCURACY 

The  accuracy  of  the  meter  has  been  fully  de- 
monstrated by  numerous  tests,  and  when  these  have 
been  made  with  the  care  that  should  be  exercised  in 
any  hydraulic  experiment,  most  satisfactory  results 
have  been  obtained. 

No  better  demonstration  of  the  accuracy  of  the 
Venturi  meter  can  be  presented  than  the  continuous 
performance  of  thirteen  meters  on  the  works  of  the 
East  Jersey  Water  Company.  That  Company  has  a 
contract  with  the  City  of  Newark,  N.  J.,  to  supply  it 
with  not  more  than  27^2  million  gallons  of  water  per 
day.  The  Company  controls  the  water  shed  and 
plant  supplying  this  water,  and  is  allowed  to  dispose  of 
the  balance  that  the  works  supply  to  other  cities  and 
towns.  In  this  way  it  supplies  at  the  present  time 
Jersey  City,  the  City  of  Bayonne,  the  Township  of 
Franklin,  the  Town  of  Montclair,  N.  J.,  and  other 
consumers.  All  the  water  is  sold  by  measure,  through 
ten  Venturi  meters,  and  daily  records  are  kept  of  the 
quantities  delivered  to  the  principal  consumers,  with 
weekly  and  monthly  records  for  the  smaller  consumers. 
Daily  records  are  also  kept  of  the  quantities  delivered 
to  the  conduits  through  receiving  meters  at  the  intake. 

The  arrangement  of  the  meters  is  shown  by 
diagram,  Fig.  n,and  the  following  table  compiled 
from  official  records  of  the  Company  shows  comparison 
of  Receiving  and  Selling  meters  for  seventeen  months. 

From   this   table   it   will  be  seen  that  in  seventeen 


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months  27,2 1 8,700,000  gallons  of  water  were  delivered 
into  the  conduits  Nos.  i  and  2,  through  two  48-inch 
intake  meters,  and  remeasured  through  ten  selling  or 
outlet  meters,  varying  in  size  from  1 2  to  48  inches,  with 
a  difference  of  measurements  between  the  two  sets  of 
meters  of  only  y2  of  i  per  cent.  Considering  only 
the  months  November,  1896,  to  July,  1897,  during 
which  performance  of  the  meters  was  not  interfered 
with  by  irregular  "  unmeasured  drafts  of  water  "  for  test- 
ing pipe  lines,  etc.,  it  will  be  seen  that  12,996,500,000 
gallons  of  water  were  measured  by  the  intake  meters 
and  remeasured  by  the  selling  meters,  with  a  difference 
of  only  17,600,000  gallons,  or  14-100  of  i  per  cent. 


12-iNCH  VENTURI  METER  TUBE,  SPIGOT  ENDS. 


26 


SETTING  OF   METER 

The  meter  tube  is  set  in  the  pipe-line,  wherever 
most  convenient.  See  Figures  5,  6,  7,  8  and  9.  The 
register  is  usually  placed  ten  feet  or  more  below  the 
hydraulic  grade,  and  not  more  than  1000  feet  from 
the  tube.  The  tube  and  register  are  connected  by 
two  lines  of  y2  inch  brass,  lead  or  tin-lined  pipe,  and 
as  a  matter  of  economy  are  usually  placed  as  near 
one  another  as  possible. 

The  register  must  be  properly  protected  from 
freezing,  and  when  a  gate-house,  pumping-station  or 
other  building  suitable  for  the  purpose  is  not  available 
a  vault  or  register  house  must  be  provided.  This 
should  be  frost  proof,  and  not  less  than  6  ft.  x  6  ft. 
inside;  but  in  other  respects  may  be  built  to  suit 
the  taste  and  requirements  of  the  purchaser.  Figures 
12,  13  14,  15  and  16  illustrate  a  few  that  have  been 
found  entirely  satisfactory.  Drawings  for  that  shown 
by  Figure  14  will  be  furnished  when  desired. 

When  the  meter  must  be  placed  where  frequent 
readings  cannot  easily  be  obtained,  the  registrations 
may  be  automatically  transmitted  by  electricity  to  a 
secondary  or  office  dial,  figure  17,  which  may  be 
placed  any  distance  from  the  register. 


c 


L 


VENTURI    METER 

BUILDERS  IRON    FOUNm 


FIGURE  17. 
SECONDARY  OR  OFFICE  DIAL. 


THE  VENTURI  WATER  METER. 


MANSFIELD  MERRIMAN'S  "HYDRAULICS." 
ARTICLE  71. 


14  It  has  been  shown  by  Herschel*  that  a  compound  tube 
provided  with  piezometers  may  be  used  for  the  accurate 
measurement  of  water.  The  apparatus,  which  is  called  by 
him  the  Venturi  Water  Meter,  is  shown  in  outline  in  the 
accompanying  figure,  and  consists  of  a  compound  tube 
terminated  by  cylinders,  into  the  top  of  which  are  tapped 


jDATUM^PLANE 


the  piezometers  Hi.  and  H ^  Surrounding  the  small  sec- 
tion #2  is  a  chamber  into  which  four  or  more  holes  lead 
from  the  top,  bottom  and  sides  of  the  tube,  and  from 

*  Transactions  American  Society  of  Civil  Engineers,  1887,  Vol.  XVIII,  p.  228. 


which  rises  the  piezometer  Hz.  The  flow  passing  through 
the  tube  has  the  velocities  vi,  Vz,  and  v3  at  the  sections  0i, 
#2,  and  a3,  and  these  velocities  are  inversely  as  the  areas  of 
the  sections.  When  the  pressure  in  a?  is  positive,  the 
water  stands  in  the  central  piezometer  at  a  height  H*,  as 
shown  in  the  figure;  when  the  pressure  is  negative  the  air 
is  rarefied,  and  a  column  of  water  lifted  to  the  height  hz. 
If  E  is  the  height  of  the  top  of  the  section  a*  above  the 
datum,  the  value  of  Hz  for  the  case  of  negative  pressure 
was  taken  to  be  E  —  hz.  The  apparatus  was  constructed 
so  that  the  areas  ai  and  a3  were  equal,  while  a2  was  about 
1-9  of  these. 

To  determine  the  discharge  per  second  through  the 
tube,  the  areas  a*  and  a*  are  to  be  accurately  found  by 
measurements  of  the  diameters  "  ;  then  (the  quantity  pass- 
ing is  equal  to  the  area  X  the  velocity  or) 

Q  =  #!  i}it  or  Q  =  a*  V?. 

If  no  losses  of  head  due  to  friction  occur  between  the  sec- 
tions a  i  and  az,  the  quantity  h'  in  the  formula  of  the  last 
article  is  o,  and 


o  = 


Inserting  in  this  for  vi  and  v*  their  values  in  terms  of 
and  then  solving  for  Q,  gives  the  result 


which  may  be  called  the  theoretic  discharge.      Dividing 
this  expression  by  a*  gives  the  velocity  vt,  and  dividing  it 

t  This  equation  is  deduced  from  the  well-known  law  that  the  sum  of  velocity  and  fric- 
tion heads  is  constant. 

36 


by  a*  gives  the  velocity  v*.  Owing  to  the  losses  of  head 
which  actually  exist,  this  expression  is  to  be  multiplied 
by  a  co-efficient  c\  thus: 


a-2 


is  the  formula  for  the  actual  discharge  per  second. 

Reference  is  made  to  Herschel's  paper,  above  quoted, 
for  a  full  description  of  the  method  of  conducting  the 
experiments.  The  discharge  was  actually  measured  either 
in  a  large  tank  or  by  a  weir;  and  thus  q  being  known  for 
observed  piezometer  heights  Hi  and  //2,the  value  of  c  was 
computed  by  dividing  the  actual  by  the  theoretic  dis- 
charge. For  example,  the  smaller  tube  used  had  the 
areas 

ai  =  0.77288,     #2  =  0.08634  square  feet; 
hence  the  theoretic  discharge  is 


Q  =  0.086884     ^  2g(Hi—  H*  ), 
and  the  co-efficient  of  discharge  or  velocity  is 


•-•§ 


In  experiment  No.  I  the  value  of  H*  was  99.069,  while 
//2  was  24. 509  feet,  and  the   actual    discharge    was    4.29 
cubic  feet  per  second.     As  .fi'was  84.704,  the  value  of  H* 
is  60.195  feet.     The  theoretic  discharge  then  is 

2  =  0.086884  X  8.02  y/38.874  =  4.345. 

Dividing  4.29  by  this,  gives  for  c  the  value  0.988.  Fifty- 
five  experiments  made  in  this  manner,  in  all  of  which 
negative  pressure  existed  in  a-2,  gave  co-efficients  ranging 

37 


in  value  from  0.94  to  1.04,  only  four  being  greater  than 
i.oi  and  only  two  less  than  0.96. 

The  larger  tube  used  had  the  areas  ai  =  57.823  and 
#2  =  7.074  square  feet,  and  the  pressure  at  the  central 
piezometer  was  both  positive  and  negative.  Twenty-eight 
experiments  give  co-efficients  ranging  from  0.95  to  0.99, 
the  highest  co-efficients  being  for  the  lowest  velocities. 
In  this  tube  the  velocity  at  the  section  #2  ranged  from  5  to 
34.5  feet  per  second.  The  small  variation  in  the  co-effi- 
cients for  the  large  range  in  velocity  indicates  that  the 
apparatus  may  in  the  future  take  a  high  rank  as  an 
accurate  instrument  for  the  measurement  of  water.  Under 
low  velocities,  however,  it  is  not  probable  that  the  arrange- 
ment of  piezometers  shown  in  the  accompanying  figure 
will  give  the  best  results ;  in  order  that  Hi  may  correctly 
indicate  the  mean  pressure  in  #i,  connection  seems  to  be 
required  both  at  the  bottom  and  sides  of  the  tube  like  that 
at  a*.  It  is  thought,  moreover,  that  the  elevation  E 
should  be  measured  to  the  centre  of  the  section  rather 
than  to  the  top.  The  lower  piezometer  H3  is  not  an 
essential  part  of  the  apparatus  and  may  be  omitted, 
although  it  was  of  value  in  the  experiments  as  showing 
the  total  loss  of  head. 


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